The standard first price and second price auctions
have been widely studied in auction theory [1]}, [2]}.
Their generalized versions for multiple items have been studied and applied in ad auctions (also called “position auctions”) [3]}, [4]}, [5]}, [6]}. Most prior works mainly discussed the Nash equilibria of the auctions or their best-response dynamics, and did not study the dynamics when players use regret minimization algorithms. One notable exception is [7]}, however, as discussed in the introduction, they analyze a different setting in which the actual play of the agents is preceded by a pure exploration phase in which all bidders bid uniformly, which leads to different convergence results than those we show in standard interaction between the algorithms.
